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Weighted composition operators induced by strongly measurable functions

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Abstract

In this paper, we describe multiplication and weighted composition operators induced by functions which either are strongly \(\mu \)-normable measurable or have strong \(\mu \)-measurability of the orbits on Lorentz–Karamata–Bochner (LKB) spaces \(L_{p,q;b}\), where \(1< p \le \infty \), \(1\le q \le \infty \) and b is a slowly varying function.

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References

  1. Arora, S.C., Datt, G., Verma, S.: Composition operators on Lorentz spaces. Bull. Aust. Math. Soc. 76(2), 205–214 (2007)

    Article  MathSciNet  Google Scholar 

  2. Arora, S.C., Datt, G., Verma, S.: Weighted composition operators on Lorentz spaces. Bull. Korean. Math. Soc. 44(4), 701–708 (2007)

    Article  MathSciNet  Google Scholar 

  3. Arora, S.C., Datt, G., Verma, S.: Multiplication and composition operators on Lorentz–Bochner spaces. Osaka J. Math. 45(3), 629–641 (2008)

    MathSciNet  MATH  Google Scholar 

  4. Blasco, O., Neerven, J.V.: Spaces of operator-valued functions measurable with respect to the strong operator topology. Opt. Theor. Adv. Appl. 201, 65–78 (2009)

    MathSciNet  MATH  Google Scholar 

  5. Blasco, O., Gregory, P.: Lorentz spaces of vector-valued measures. J. Lond. Math. Soc. 67(3), 739–751 (2003)

    Article  MathSciNet  Google Scholar 

  6. Bu, Q., Lin, P.K.: Radon–Nikodym property for the projective tensor product on Kothe function spaces. J. Math. Anal. Appl. 293(1), 149–159 (2004)

    Article  MathSciNet  Google Scholar 

  7. Bennett, C., Sharpley, R.: Interpolation of operators, Pure and Applied Mathematics. Academic, Boston (1988)

    MATH  Google Scholar 

  8. Cui, Y., Hudzik, H., Kumar, R., Maligranda, L.: Composition operators on Orlicz spaces. J. Aust. Math. Soc. 76(2), 189–206 (2004)

    Article  MathSciNet  Google Scholar 

  9. Datt, G., Arora, S.C.: Injective composition operators on Lorentz–Bochner spaces. Demonstr. Math. 46(4), 741–756 (2013)

    MathSciNet  MATH  Google Scholar 

  10. Datt, G., Chugh, R., Jakhar, J.: A note on multiplication operators between Lorentz–Karamata spaces. Br. J. Math. Comput. Sci. 11(2), 1–10 (2015)

    Article  Google Scholar 

  11. Edmunds, D.E., Evans, W.D.: Hardy operators, function spaces and embeddings, Springer Monographs in Mathematics. Springer, Berlin (2004)

    Book  Google Scholar 

  12. Eryilmaz, I.: Multiplication operators on Lorentz-Karamata-Bochner spaces. Math. Slovaka 62(2), 293–300 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Hunt, R.A.: On \(L_{(p; q)}\) spaces. Enseignement Math. 12(2), 249–276 (1966)

    MathSciNet  MATH  Google Scholar 

  14. Komal, B.S., Gupta, S.: Multiplication operators between Orlicz spaces. Integral Equ. Oper. Theory 41(3), 324–330 (2001)

    Article  MathSciNet  Google Scholar 

  15. Kumar, R., Kumar, R.: Composition operators on Banach function spaces. Proc. Am. Math. Soc. 133(7), 2109–2118 (2005)

    Article  MathSciNet  Google Scholar 

  16. Kwessi, E., Alfonso, P., Souza, G.D., Abebe, A.: A note on multiplication and composition operators in Lorentz spaces. J. Funct. Spaces Appl. Article ID 2936, 1–10 (2012)

    Article  MathSciNet  Google Scholar 

  17. Nakai, E.: Pointwise multipliers on the Lorentz spaces. Mem. Osaka Kyoiku Univ. III Natur. Sci. Appl. 45(1), 1–7 (1996)

    MathSciNet  Google Scholar 

  18. Neves, J.S.: Lorentz–Karamata spaces, Bessel and Riesz potentials and embeddings. Diss. Math. (Rozprawy Mat.) 405, 46 (2002)

    MathSciNet  MATH  Google Scholar 

  19. Singh, R.K., Manhas, J.S.: Composition operators on function spaces, North-Holland Mathematics Studies, vol. 179. North-Holland Publishing Co., Amsterdam (1993)

    Chapter  Google Scholar 

  20. Takagi, H., Yokouchi, K.: Multiplication and composition operators between two \(L_p\) spaces, vol. 232, pp. 321–338. Amer. Math. Soc., Providence (1999)

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Acknowledgements

Suggestions of the referee(s), in forming the paper in the present form, are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, PGDAV College, University of Delhi, Delhi, 110065, India

    Gopal Datt

  2. Department of Mathematics, M.D. University, Rohtak, Haryana, 124001, India

    Renu Chugh & Jagjeet Jakhar

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  1. Gopal Datt
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  2. Renu Chugh
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  3. Jagjeet Jakhar
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Correspondence to Gopal Datt.

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Datt, G., Chugh, R. & Jakhar, J. Weighted composition operators induced by strongly measurable functions. Afr. Mat. 29, 995–1006 (2018). https://doi.org/10.1007/s13370-018-0596-y

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  • DOI: https://doi.org/10.1007/s13370-018-0596-y

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